Generalized chain-rule forms for JEE

Formula

\[\frac{d}{dx}[u(x)]^n=n[u(x)]^{n-1}u'(x),\qquad \frac{d}{dx}\sin u=\cos u\,u',\qquad \frac{d}{dx}e^{u}=e^{u}u'\]

Variables: \(u=u(x)\), \(n\in\mathbb R\).

Conditions: Where expressions are defined and differentiable.

Quick application of chain rule.